A graph of velocity vs. time of a ship coming into a harbor is shown below. (a) Describe the motion of the ship based on the graph. (b)What would a graph of the ship's acceleration look like?
(a) The ship moves at constant velocity and then begins to decelerate at a constant rate. At some point, its deceleration rate decreases. It maintains this lower deceleration rate until it stops moving.
(b) A graph of acceleration vs. time would show zero acceleration in the first leg, large and constant negative acceleration in the second leg, and constant negative acceleration.
Graphical solutions yield identical solutions to mathematical methods for deriving motion equations.
The slope of a graph of displacement
vs. time
is velocity
.
The slope of a graph of velocity
vs. time
graph is acceleration
.
Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.
Conceptual questions
(a) Explain how you can use the graph of position versus time in
[link] to describe the change in velocity over time. Identify (b) the time (
,
,
,
, or
) at which the instantaneous velocity is greatest, (c) the time at which it is zero, and (d) the time at which it is negative.
(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in
[link] . (b) Identify the time or times (
,
,
, etc.) at which the instantaneous velocity is greatest. (c) At which times is it zero? (d) At which times is it negative?
(a) Explain how you can determine the acceleration over time from a velocity versus time graph such as the one in
[link] . (b) Based on the graph, how does acceleration change over time?
(a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in
[link] . (b) Identify the time or times (
,
,
, etc.) at which the acceleration is greatest. (c) At which times is it zero? (d) At which times is it negative?
Consider the velocity vs. time graph of a person in an elevator shown in
[link] . Suppose the elevator is initially at rest. It then accelerates for 3 seconds, maintains that velocity for 15 seconds, then decelerates for 5 seconds until it stops. The acceleration for the entire trip is not constant so we cannot use the equations of motion from
Motion Equations for Constant Acceleration in One Dimension for the complete trip. (We could, however, use them in the three individual sections where acceleration is a constant.) Sketch graphs of (a) position vs. time and (b) acceleration vs. time for this trip.
A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.
Note: There is always uncertainty in numbers taken from graphs. If your answers differ from expected values, examine them to see if they are within data extraction uncertainties estimated by you.
(a) By taking the slope of the curve in
[link] , verify that the velocity of the jet car is 115 m/s at
. (b) By taking the slope of the curve at any point in
[link] , verify that the jet car's acceleration is
.
Using approximate values, calculate the slope of the curve in
[link] to verify that the velocity at
is 0.208 m/s. Assume all values are known to 3 significant figures.
Using approximate values, calculate the slope of the curve in
[link] to verify that the velocity at
is 0.238 m/s. Assume all values are known to 3 significant figures.
Construct the displacement graph for the subway shuttle train as shown in
[link] (a). Your graph should show the position of the train, in kilometers, from t = 0 to 20 s. You will need to use the information on acceleration and velocity given in the examples for this figure.
(a) Take the slope of the curve in
[link] to find the jogger's velocity at
. (b) Repeat at 7.5 s. These values must be consistent with the graph in
[link] .
A graph of
is shown for a world-class track sprinter in a 100-m race. (See
[link] ). (a) What is his average velocity for the first 4 s? (b) What is his instantaneous velocity at
? (c) What is his average acceleration between 0 and 4 s? (d) What is his time for the race?
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product